Anyway they're in really nice condition externally but storage in cold and humid conditions combined with apparently having had the cone pushed in during this storage has resulted in the spider being stuck in a position that isn't in the middle... They move nicely but the travel inwards is much shorter than outwards.
Is there anything I can do? I've been running them for a few hours with a 20hz sine wave on low level but it hasn't made a difference.

An unusual situation, and I don't know how an expert would approach the problem. I'm thinking that low level 20Hz wouldn't be as helpful as just exercising the spider with a higher level music signal, maybe directing steam at the spider before that is done.

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It is error only, and not truth, that shrinks from enquiry. - Thomas Paine

freddi's suggestion seems reasonable and worth a try before reconing them

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First of all, got the link wrong, but they're 25F EW's even though it doesn't make a difference.

I've been driving them with sine and music at decent levels but the spider still returns to an offset location..
I just jammed one driver with a toilet paper roll (carefully) and I don't think it will help on its own but I might as well try giving it some heat. They are virtually unusable in their current state but I have nothing to lose.
I doubt SEAS will have any reconing kits or can help at all because this driver is listed in their "Very old vintage drivers"...